Seismic assessment of masonry structures through an energy-based approach

Topology optimization is widely used in structural design to achieve optimal load paths that may be conveniently adopted to cope with the construction of truss-like structures or to arrange layout of reinforcing material based on the minimization of the overall strain energy. Procedures that implement the minimization of the strain energy may be also adopted to solve equilibrium equations for bodies admitting an energy functional, that is, for hyperelastic materials. The no-tension model is often adopted within preliminary analysis tool to cope with the negligible strength in tension that is peculiar to many kinds of masonry-like materials. Notwithstanding the simplicity of such a theoretical method [1, 2], its numerical implementation is not trivial. Most of the strategies available in the literature resort to non-linear finite element techniques that are frequently affected by convergence losses due to the no-tension constraint [3]. An alternative numerical approach is implemented for the analysis of no-tension masonry-like solids, that is based on a topology optimization approach [4]. The equilibrium of a two-dimensional hyperelastic no-tension body is found searching for the distribution of an equivalent orthotropic material, in which tensile principal stresses are not allowed by prescribing negligible stiffness in the relevant direction, such that the potential energy of the solid is minimized, see also [5]. Unlike many conventional approaches that deal with the inherent non-linearity of the problem through step-wise incremental analysis, the adopted energy-based method efficiently solves the effect of compatible loads through a one-shot optimization. The method is ideally conceived to cope with the seismic assessment of masonry structures, since, for any prescribed load, a single optimization run is able to solve the equilibrium equation and to evaluate the structural safety. A benchmark from the literature is investigated to assess the effectiveness of the proposed procedure and to point out possible applications inspired by the limit analysis of masonry-like structures subject to earthquake loads.